Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
//package Codeforces.Round717Div2;

import java.io.*;
import java.util.*;

public class C {
    public static void main(String[] args) throws IOException {
        Soumit sc = new Soumit();

        int n = sc.nextInt();
        int[] arr = sc.nextIntArray(n);
        int[] copyarr = new int[n];
        ArrayList<Queue<Integer>> arlist = new ArrayList<>();
        for(int i=0;i<2020;i++){
            arlist.add(new LinkedList<>());
        }
        for(int i=0;i<n;i++){
            arlist.get(arr[i]).add(i);
        }
        System.arraycopy(arr, 0, copyarr, 0, n);

        int sum = 0;
        for(int i=0;i<n;i++){
            sum += arr[i];
        }
        sc.sort(arr);

        long[][] dp = new long[n+1][sum+5];
        for(int i=0;i<=n;i++){
            for(int j=0;j<dp[0].length;j++){
                dp[i][j] = Long.MAX_VALUE;
            }
        }
        for(int i=0;i<=n;i++){
            dp[i][0] = 0;
        }
        for(int i=1;i<=n;i++){
            for(int j=0;j<dp[0].length;j++){
                if(j-arr[i-1]>=0 && dp[i-1][j-arr[i-1]]!=Long.MAX_VALUE){
                    dp[i][j] = Math.min(dp[i][j-arr[i-1]]+1, dp[i-1][j]);
                }
                else{
                    dp[i][j] = dp[i-1][j];
                }
            }
        }

        /*for(long[] i: dp){
            System.out.println(Arrays.toString(i));
        }*/

        if(sum%2==1 || dp[n][sum/2]==Long.MAX_VALUE){
            System.out.println(0);
        }
        else{
            int goodval = 0;
            long goodcount = Long.MAX_VALUE;
            for(int i=1;i<dp[0].length;i++){
                if(dp[n][i]>0 && dp[n][i]!=Long.MAX_VALUE && ((sum-i)%2!=0 || dp[n][(sum-i)/2]==Long.MAX_VALUE)){
                    if(dp[n][i]<goodcount){
                        goodval = i;
                        goodcount = dp[n][i];
                    }
                }
            }

            System.out.println(goodcount);
            ArrayList<Integer> list = new ArrayList<>();
            int i = dp.length-1;
            int j = goodval;
            while(i!=0){
                if(dp[i][j]==dp[i-1][j]){
                    i--;
                }
                else{
                    j-=arr[i-1];
                    list.add(arr[i-1]);
                    i--;
                }
            }

            Collections.sort(list);
            for(i=0;i<list.size();i++){
                Queue<Integer> q = arlist.get(list.get(i));
                System.out.print((q.remove()+1)+" ");
            }
            System.out.println();
        }

        sc.close();
    }

    static class Soumit {
        final private int BUFFER_SIZE = 1 << 18;
        final private DataInputStream din;
        final private byte[] buffer;
        private PrintWriter pw;
        private int bufferPointer, bytesRead;
        StringTokenizer st;

        public Soumit() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Soumit(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public void streamOutput(String file) throws IOException {
            FileWriter fw = new FileWriter(file);
            BufferedWriter bw = new BufferedWriter(fw);
            pw = new PrintWriter(bw);
        }

        public void println(String a) {
            pw.println(a);
        }

        public void print(String a) {
            pw.print(a);
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[3000064]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public void sort(int[] arr) {
            ArrayList<Integer> arlist = new ArrayList<>();
            for (int i : arr)
                arlist.add(i);

            Collections.sort(arlist);
            for (int i = 0; i < arr.length; i++)
                arr[i] = arlist.get(i);
        }

        public void sort(long[] arr) {
            ArrayList<Long> arlist = new ArrayList<>();
            for (long i : arr)
                arlist.add(i);

            Collections.sort(arlist);
            for (int i = 0; i < arr.length; i++)
                arr[i] = arlist.get(i);
        }

        public int[] nextIntArray(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }

            return arr;
        }

        public long[] nextLongArray(int n) throws IOException {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }

            return arr;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] arr = new double[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextDouble();
            }

            return arr;
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            /*if (din == null)
                return;*/
            if (din != null) din.close();
            if (pw != null) pw.close();
        }
    }
}